Video Description

To fully utilise the exciting category theory we've learnt so far, we need a way to abstract definitions from a specific category and then be able to apply them in any category we want. The solution to this is universal construction. This video will explore the process of universal construction and see it used in practice, which will further expose some elegant relationships between categories that we've seen before. Taking examples from mathematical proofs, functional programming and beyond, this is the next major step into abstraction that our category theory journey takes us. ― Timestamps ― 0:00 - Intro 1:03 - Isomorphism 5:22 - Terminal object 10:41 - Universal construction 12:27 - Conjunction 17:32 - Product 18:29 - Pair type 24:12 - Outro 25:00 - Exercise ― Credits ― All animation and voiceover created by Eyesomorphic. Background music: 'Sonder', composed by Caleb Peppiatt. ― Further Reading ― Category Theory and Why We Care, by Eyesomorphic (Lecture series): https://youtube.com/playlist?list=PLoCKNPo3VR0I2wqT2wemCNIlpjdy_Ry_q&si=9UOLXRFqNdfgGXlI Algebra: Chapter 0 (Book), by Paulo Aluffi